A is half of B and B is half of C. If the average of A,B,C, is 70, find the value of A.

Question

A is half of B and B is half of C. If the average of A,B, and C is 70, find the value of A.

 

Answer 1

From the problem we can see that both A and C can be expressed in terms of B:

    A = B / 2

    B = C / 2 or C = 2B

    Now the average of A and B anc C is given as 70

    Equation expressing the average:  (A + B + C) / 3 = 70

    Plugging in expressions for A and C in terms of B:  (B/2 + B + 2B) / 3 = 70

    Multiplying both sides of equation by 3:  B/2 + B + 2B = 210

    Multiplying both sides of equation by 2 to get rid of fraction on left side:  B + 2B + 4B = 420

    Combing B terms on left side:  7B = 420

    Dividing both sides of equation by 7 to get value of B:  B = 60

    Plug in value for B in B expression for A:  A = B / 2 = 60 / 2 = 30  

Answer 2

Consider this, let A = 1, then B= 2 and C= 4, their total is 1+2+4=7. The average of 3 numbers is 70; their total is 70 x 3 =210. So if A =1 the total is 7 what value of A will make the total 210? That valueis 210/7 = 30.

Answer 3

Roman has the value for A correct but it would help if you also obtain the values for B and C and check your work. A key point of the problem as you mentioned in your reply to Allison is that the average value is 70 which means that (A + B + C)/3 = 70. The equations need to be rewritten to take this into account like so: (C/4 + C/2 + C)/3 = 70 which gives

 (C/4 + 2C/4 + 4C/4) = 210 after multiplying both sides by 3 and getting the fractions with the same denominator. Adding the 3 fractions gives 7C/4 = 210 and multiplying each side by 4 gives 7C = 840 which results in C = 120 ; B = C/2 = 60; A = B/2 = C/4 = 30. Check your work by getting the average like so (120+60+30)/3 = 70. Best wishes.

Answer 4

You can use substitution so that you are only solving for one variable at a time.

So C = C ,  B = C/2 ,  and A = B/2 = C/4

Plug these values into (A + B + C)/3 = 70

You get  (C) + (C/2) + (C/4) = 210

Multiply both sides of the equation by 4 to get rid of the fractions 

4C + 2C  + C = 840

Now solve for C by combining your like terms 

7C = 840 

C = 120 

Now plug that value into your orginal values 

C = 120 ,  B = C/2 = 60 , and A = B/2 = C/4 = 30 

Lastly, check your answer 

(A + B + C)/3 = 70 

(30 + 60 + 120)/3 = 70 

Always make sure your answer makes sense with the quesiton asked

Good Luck and I hope that helps! 

Answer 5

You have a nice problem. Just write down what it says and then we will solve it step by step.

1. A=B/2,

2. B=C/2

3. (A+B+C)/3=70  (Since its average of the three)

Since there is only one equaltion with a numerical value, thereofre we have to use this eaualtion to find out the value of A, B and C but we can't solve three variables from only one equation. We will substitute values of two other variabe to the third variable in the equation.  As we see, all A,B and C-ther are related, we will try to replace 2 of them in eq.3 and make it only one varible.

From eq.1 above, A=B/2

or, 2A=B

Again, B=C/2, so, We put C/2 above and get, 2A=C/2

or, A=C/4

So now we see, all variabe can be expressed in terms of C only. So we substitute variables A and B in the main eq. 3 and write in terms of C,

 

So, A+B+C=70X3 (multiplied both sides with 3)

or, we can write, C/4+C/2+C=210 (from eq. 1 and 2 above)

or, (C+2C+4C)/4=210

or, 7C/4=210

or, 7C=210X4

or, C=210X4/7=30X4=120

Therefore, C=120

B=C/2=60

and, A=B/2=60/2=30

 

Answer 6

We have B=2A and C=2B so C=2(2A)=4A. So substitute:

(A+B+C)/3 = 70

(A+2A+4A)/3=70

7A/3=70

A=70*3/7=30